Here is a drill program that will improve the essential skills for any intermediate algebra student. This is an exercise in the factoring of quadratic expressions. Such an expression can be written as the product of 2 factors, each factor consisting of 2 terms: an x to the first power term and a constant term. In the Solvequad app these 4 coefficients are randomly chosen integers from 1 to 6.
The top/first line of the Solvequad screen presents the quadratic expression. The second line shows the skeletons of the 2 factors that produce this expression, with 4 blank gray buttons for the 4 unknown coefficients. The user enters the numbers for these coefficients using the virtual keypad. This keypad has only the needed digits, 1 – 6, a minus sign, a delete key and a done key. The small number of keys means that the individual keys can be nice and large, minimizing entry errors. Accidental errors that do occur can be quickly corrected with the delete key. The selection of the coefficients to enter is made either by tapping the appropriate gray button, or by tabbing through the 4 buttons.
The third line on the screen shows the quadratic expression calculated as the coefficients are entered. This automatic calculation saves the user the trouble, so that he/she can concentrate on deciding which values to enter for the coefficients. After all 4 coefficients have been entered the student can compare the calculated quadratic expression in the third line with the problem quadratic expression in the first line. Any discrepancies can be corrected by re-entering the any of the coefficients of the factors. (second line of the screen). The done key is tapped when the user is satisfied that the first and third line quadratic expressions are the same. If the expressions are not the same the user is charged with an error and is told to re-enter the factor coefficients until the correct quadratic expression is calculated. This policy makes if easy for the student to avoid errors. The real strategy is to finish quickly by doing the correct coefficient calculation mentally so that there is no need to re-enter. The current version of the program does not track the completion time, but that capability can be added if there is sufficient interest.
Factoring a quadratic expression leads directly to solving for the 2 roots of the equation made by setting the quadratic expression equal to zero (values of x that make the quadratic expression equal to zero), hence the app name: Solvequad. The quadratic expression will equal zero when either of the 2 factors equals zero, so the roots of the quadratic expression are the 2 values of x that will make either of the 2 factors equal to zero. To the student of intermediate algebra this last step (solving a simple linear equation in one unknown) is trivial; it is left out of this app to limit the app to one process/algorithm and to avoid boring the user with trivia.
Tags: complex quadratic equation algorithm